What do Moses's songs mean?

At the end of Deuteronomy, the host of Israelites are approaching the promised land to which God has led them, and Moses prepares to die since he will not be allowed into Canaan. Moses sings two songs as a final parting blessing to the people he has helped lead since their time in Egypt, but what exactly do these blessings mean?

"Give ear, O heavens, and I will speak,
and let the earth hear the words of my mouth.
May my teaching drop as the rain,
my speech distill as the dew,
like gentle rain upon the tender grass,
and like showers upon the herb.
For I will proclaim the name of the LORD;
ascribe greatness to our God! (Deuteronomy 32:1-3)"

In the Song of Moses, he opens with the similes of His teachings being as the rain and dew, falling to earth to refresh the Israelites before he departs, and leads into God's condemnation of the other peoples of the Earth, that they have angered Him by being corrupt and blemished. He reminds the Israelites that no god but the one true God helped them throughout their years of wandering in the wilderness.

He then recounts the stubbornness and unfaithfulness of the Israelites in their ordeals, how they forgot the "Rock" that bore them and came to resent it, and began to worship other gods that never existed and demons who set them against the true God, which kindled God's anger and threatened to destroy them. He laments their sins, and reminds them that in the end, if they abandon Him, then He will abandon them:

Then he will say, 'Where are their gods,
the rock in which they took refuge,
who ate the fat of their sacrifices
and drank the wine of their drink offering?
Let them rise up and help you;
let them be your protection! (Deuteronomy 32:37-338)

He seeks to remind the Israelites that there is only one God, and to remain faithful to him, for he will stand with them against their enemies and "repay those who hate me (Deut. 32:41)."

The LORD came from Sinai
and dawned from Seir upon us;
he shone forth from Mount Paran;
he came from the ten thousands of holy ones,
with flaming fire at his right hand.

Afterwards, Moses is called by God to Mount Nebo, to look upon Canaan, the promised land, before he dies. In his last moments Moses blesses the tribes of Israel with his second poem. He starts by briefly recounting the beginnings of their journey and trails since Mount Sinai, then moves on to bless the tribes of Israel.

"Let Reuben live, and not die,
but let his men be few."
And this he said of Judah:
Hear, O LORD, the voice of Judah,
and bring him in to his people.
With your hands contend for him,
and be a help against his adversaries." (Deuteronomy 33:6-7)

Here is a simple prayer for Reuben to live and not die, while Moses asks God to fight for Judah against their enemies. Moses tells that the tribe of Levi will be the ones teaching and upholding God's laws, and for Him to crush their adversaries so that they may not rise again. The tribe of Benjamin is beloved by God and protected by Him. Moses blesses the land of the tribe of Joseph, so that it will provide them with the best food and give them plenty. Zebulun and Issachar are blessed with the abundance of the sea. Gad chose the best land for himself and will execute the justice of the Lord, Dan is compared to a lion's cub, Naphtali is given the west and the south, and Asher will have bars of iron and bronze.

At the end, all of Israel is blessed by Moses to be protected by God wherever the go under His bidding, to tread upon the backs of their enemies as they march through their promised land.